How to bake AO + Diffuse into one map in cycles?
Generally, you do not want to do this for AO, see Adding Ambient Occlusion to Material

However, if you really want to in this case, you can just bake the diffuse channel. Since you multiplied AO into diffuse, it is now part of diffuse. So just bake that. If you don't want to also include lighting, set bake type to "diffuse" and bake only the color pass:



(remember, however, by multiplying AO over diffuse, you are already "including lighting" as AO is lighting, not color)